Category:Definitions/Convergent Sequences
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This category contains definitions related to Convergent Sequences.
Related results can be found in Category:Convergent Sequences.
Topological Space
Let $T = \struct {S, \tau}$ be a topological space.
Let $A \subseteq S$.
Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence in $A$.
Then $\sequence {x_n}$ converges to the limit $\alpha \in S$ if and only if:
- $\forall U \in \tau: \alpha \in U \implies \paren {\exists N \in \R_{>0}: \forall n \in \N: n > N \implies x_n \in U}$
Subcategories
This category has the following 8 subcategories, out of 8 total.
B
C
Pages in category "Definitions/Convergent Sequences"
The following 19 pages are in this category, out of 19 total.
C
- Definition:Convergent Rational Sequence
- Definition:Convergent Real Sequence
- Definition:Convergent Sequence
- Definition:Convergent Sequence in Normed Vector Space
- Definition:Convergent Sequence/Also known as
- Definition:Convergent Sequence/Analysis
- Definition:Convergent Sequence/Complex Numbers
- Definition:Convergent Sequence/Metric Space
- Definition:Convergent Sequence/Normed Division Ring
- Definition:Convergent Sequence/Normed Vector Space
- Definition:Convergent Sequence/Notation
- Definition:Convergent Sequence/Note on Domain of N
- Definition:Convergent Sequence/P-adic Numbers
- Definition:Convergent Sequence/Rational Numbers
- Definition:Convergent Sequence/Real Numbers
- Definition:Convergent Sequence/Test Function Space
- Definition:Convergent Sequence/Topology
- Definition:Converging Sequence